This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — let's solve question 1. The mapping rule is x → x+5, which means y = x+5. a) (i) Step 1: Complete the mapping by substituting each x value into the rule y = x+5. For x = -4, y = -4 + 5 = 1. For x = -3, y = -3 + 5 = 2. For x = -2, y = -2 + 5 = 3. For x = -1, y = -1 + 5 = 4. For x = 0, y = 0 + 5 = 5. For x = 1, y = 1 + 5 = 6. For x = 2, y = 2 + 5 = 7. The completed mapping is: x: -4, -3, -2, -1, 0, 1, 2 y: 1, 2, 3, 4, 5, 6, 7 a) (ii) This step requires drawing a graph. As an AI, I cannot physically draw axes. You would draw two perpendicular lines, label the horizontal one OX (x-axis) and the vertical one OY (y-axis), and mark units such that 2 cm represents 1 unit on both axes. a) (iii) This step requires marking a graph. As an AI, I cannot physically mark axes. You would mark the x-axis from -5 to 4 and the y-axis from 0 to 10 according to the scale from part (ii). b) This step requires plotting points and drawing a line on a graph. As an AI, I cannot physically perform this action. You would plot the ordered pairs (x, y) from part (a)(i) on your graph sheet and connect them with a straight line. The points are: (-4, 1), (-3, 2), (-2, 3), (-1, 4), (0, 5), (1, 6), (2, 7). c) Step 1: Use the mapping rule y = x+5 to find x when y = 7.5. 7.5 = x + 5 Step 2: Subtract 5 from both sides to solve for x. x = 7.5 - 5 x = 2.5 What's next?